This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker–Campbell–Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or the heat kernel is introduced with a new computational algorithm which will be useful for the inference for diffusion processes. The approximation is regarded as the splitting around the Euler–Maruyama scheme for the density. Numerical examples for diffusion processes are shown to validate the proposed scheme.
Accepté le :
Publié le :
DOI : 10.1051/m2an/2020043
Keywords: Heat kernel, high order discretization, operator splitting, Baker–Campbell–Hausdorff formula, Malliavin calculus
@article{M2AN_2021__55_S1_S323_0,
author = {Iguchi, Yuga and Yamada, Toshihiro},
title = {Operator splitting around {Euler{\textendash}Maruyama} scheme and high order discretization of heat kernels},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {S323--S367},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {Suppl\'ement},
doi = {10.1051/m2an/2020043},
mrnumber = {4221306},
zbl = {1479.58024},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2020043/}
}
TY - JOUR AU - Iguchi, Yuga AU - Yamada, Toshihiro TI - Operator splitting around Euler–Maruyama scheme and high order discretization of heat kernels JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - S323 EP - S367 VL - 55 IS - Supplément PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2020043/ DO - 10.1051/m2an/2020043 LA - en ID - M2AN_2021__55_S1_S323_0 ER -
%0 Journal Article %A Iguchi, Yuga %A Yamada, Toshihiro %T Operator splitting around Euler–Maruyama scheme and high order discretization of heat kernels %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P S323-S367 %V 55 %N Supplément %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2020043/ %R 10.1051/m2an/2020043 %G en %F M2AN_2021__55_S1_S323_0
Iguchi, Yuga; Yamada, Toshihiro. Operator splitting around Euler–Maruyama scheme and high order discretization of heat kernels. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021), pp. S323-S367. doi: 10.1051/m2an/2020043
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